Abstract Kelvin-Noether theorems for Lie group extensions

DOI10.1007/s11005-008-0246-7zbMath1190.37083OpenAlexW1980267750WikidataQ115381909 ScholiaQ115381909MaRDI QIDQ1024858

Cornelia Vizman

Publication date: 17 June 2009

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-008-0246-7

zbMATH Keywords

geodesic equationEuler-Poincaré equationcentral and abelian extensionKelvin-Noether quantity

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Geometric theory, characteristics, transformations in context of PDEs (35A30) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65)

Cites Work

• The geometric structure of complex fluids
• Korteweg - de Vries suoerequation as an Euler equation
• Infinite dimensional Lie transformation groups
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensor-densities on \(S^1\)
• Central extensions of infinite-dimensional Lie algebras and Lie groups, Virasoro algebra and generalizations
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Central extensions of semidirect products and geodesic equations
• Groups of diffeomorphisms and the motion of an incompressible fluid
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Geodesics on extensions of Lie groups and stability: The superconductivity equation
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